Finite Group Databasebeta

← #14650244

Subgroups — #14650244

Order 2816.

750 conjugacy classes of subgroups.

The subgroup lattice has 494 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622653C211yesmaximal, characteristic
2C22⋊C4×Dic22C211yesmaximal, characteristic, complemented
3#13068550C211yesmaximal, characteristic, complemented
4#13067184C211yesmaximal, characteristic
5#13066483C211yesmaximal, characteristic, complemented
6#13066464C211yesmaximal, characteristic, complemented
7C11×#1964C211yesmaximal, characteristic
8C23×Dic22C2211yescharacteristic
9C2×C11×#121C2211yescharacteristic
10C22×#4324C412yescomplemented
11C2×C4×Dic22—21no—
12C2×C11×#99—21no—
13C2×C11×#99—21no—
14C11×#380C2211yescharacteristic
15C4×C11×C22⋊C4C2211yescharacteristic
16#10622825C2211yescharacteristic
17C2×C22⋊(C11⋊C8)C2211yescharacteristic
18C2×C22⋊(C11⋊C8)C2211yescharacteristic
19#10622653—21no—
20#10622653—22no—
21#10622653—21no—
22C2×#66874—22no—
23C2×#66874C412yescomplemented
24#10622555—21no—
25C22⋊C4×Dic11—21no—
26#10622542—21no—
27#10622259—22no—
28#10622175—22no—
29C22×D4×C11—21no—
30C22×D4×C11C2×C411yescharacteristic
31C23×C4×C11C2311yescharacteristic
32C23×Dic11—21no—
33C22×Dic22—21no—
34C22×Dic22—21no—
35C22×Dic22—21no—
36C22×Dic22—44no—
37C22×Dic22C2×C412yes—
38C22×Dic22D411yescharacteristic
39C22×Dic22D412yes—
40C22×Dic22D411yescharacteristic
41C11×#121—21no—
42C11×#121—21no—
43C11×#121—21no—
44C11×#121—21no—
45C2×C11×C4⋊C4—21no—
46C2×C11×C4⋊C4C2×C411yescharacteristic
47C2×C11×C22⋊C4—21no—
48C2×C11×C22⋊C4—21no—
49C2×C11×C22⋊C4D411yescharacteristic
50C2×C11×C22⋊C4D411yescharacteristic
51C2×C42×C11—21no—
52C2×C22⋊Dic11—21no—
53C2×#4324—22no—
54C2×#4324—22no—
55C2×#4324—44no—
56C2×C4⋊Dic11—21no—
57C2×Dic11⋊C4—22no—
58C2×C4×Dic11—22no—
59C22×C11⋊C8—21no—
60C22×C11⋊C8C2×C412yes—
61C4×Dic22—44no—
62C11×#99—42no—
63C11×#99—42no—
64C11×#95—21no—
65C11×#95—21no—
66C11⋊#95—22no—
67C11⋊#95—22no—
68C11⋊#95D412yes—
69C22⋊(C11⋊C8)—21no—
70C22⋊(C11⋊C8)—21no—
71C22⋊(C11⋊C8)—21no—
72C22⋊(C11⋊C8)—21no—
73#66874—22no—
74#66874—22no—
75#66874—44no—
76#9262—111nomaximal, Sylow
77C24×C11—21no—
78C24×C11C2×D411yescharacteristic
79C2×D4×C11—21no—
80C2×D4×C11—21no—
81C2×D4×C11—42no—
82C2×D4×C11—41no—
83C2×D4×C11—41no—
84C2×D4×C11—41no—
85C2×D4×C11—41no—
86C2×D4×C11—41no—
87C2×D4×C11—41no—
88C22×C4×C11—21no—
89C22×C4×C11—21no—
90C22×C4×C11—21no—
91C22×C4×C11—42no—
92C22×C4×C11—41no—
93C22×C4×C11C22×C411yescharacteristic
94C22×C4×C11C2×D411yescharacteristic
95C22×C4×C11C2×D411yescharacteristic
96C22×C4×C11C2×D411yescharacteristic
97C22×C4×C11#4111yescharacteristic
98C22×C4×C11#4111yescharacteristic
99C22×Dic11—22no—
100C22×Dic11—21no—
101C22×Dic11—21no—
102C22×Dic11—22no—
103C22×Dic11—22no—
104C22×Dic11—44no—
105C2×Dic22—24no—
106C2×Dic22—24no—
107C2×Dic22—24no—
108C2×Dic22—22no—
109C2×Dic22—22no—
110C2×Dic22—21no—
111C2×Dic22—21no—
112C2×Dic22—42no—
113C2×Dic22—42no—
114C2×Dic22—42no—
115C2×Dic22—44no—
116C2×Dic22—44no—
117C2×Dic22—44no—
118C2×Dic22C22⋊C412yes—
119C2×Dic22C22⋊C412yes—
120C11×C4⋊C4—21no—
121C11×C4⋊C4—21no—
122C11×C4⋊C4—42no—
123C11×C22⋊C4—21no—
124C11×C22⋊C4—21no—
125C11×C22⋊C4—21no—
126C11×C22⋊C4—41no—
127C11×C22⋊C4—41no—
128C11×C22⋊C4—41no—
129C11×C22⋊C4—41no—
130C11×C22⋊C4SD1612yescomplemented
131C42×C11—42no—
132C22⋊Dic11—41no—
133C22⋊Dic11—41no—
134#4324—44no—
135#4324—44no—
136C4⋊Dic11—42no—
137Dic11⋊C4—44no—
138C4×Dic11—44no—
139C2×C11⋊C8—22no—
140C2×C11⋊C8—42no—
141C2×C11⋊C8—42no—
142C2×C11⋊C8—41no—
143C2×#448—111no—
144Q8×C22⋊C4—111no—
145#1964D1111yescharacteristic
146#1787—111no—
147#1519—111no—
148#1289—111no—
149#1282—111no—
150C23×C11—41no—
151C23×C11—41no—
152C23×C11—41no—
153C23×C11—41no—
154C23×C11—41no—
155C23×C11—81no—
156C23×C11—81no—
157C23×C11C4×D411yescharacteristic
158C23×C11#12011yescharacteristic
159C23×C11#12111yescharacteristic
160C23×C11C2×SD1611yescharacteristic
161C23×C11#13511yescharacteristic
162C23×C11AGL(1,ℤ/8)11yescharacteristic
163C23×C11#13711yescharacteristic
164D4×C11—42no—
165D4×C11—81no—
166D4×C11—81no—
167D4×C11—81no—
168D4×C11—81no—
169D4×C11—81no—
170C2×C4×C11—22no—
171C2×C4×C11—22no—
172C2×C4×C11—22no—
173C2×C4×C11—22no—
174C2×C4×C11—41no—
175C2×C4×C11—41no—
176C2×C4×C11—41no—
177C2×C4×C11—41no—
178C2×C4×C11—41no—
179C2×C4×C11—41no—
180C2×C4×C11—41no—
181C2×C4×C11—41no—
182C2×C4×C11—41no—
183C2×C4×C11—41no—
184C2×C4×C11—41no—
185C2×C4×C11—81no—
186C2×C4×C11—81no—
187C2×C4×C11—81no—
188C2×C4×C11C2×C22⋊C411yescharacteristic
189C2×C4×C11C4×D411yescharacteristic
190C2×C4×C11#12111yescharacteristic
191C2×C4×C11#12311yescharacteristic
192C2×Dic11—24no—
193C2×Dic11—22no—
194C2×Dic11—22no—
195C2×Dic11—44no—
196C2×Dic11—44no—
197C2×Dic11—42no—
198C2×Dic11—42no—
199C2×Dic11—42no—
200C2×Dic11—42no—
201Dic22—24no—
202Dic22—22no—
203Dic22—22no—
204Dic22—22no—
205Dic22—44no—
206Dic22—44no—
207Dic22—42no—
208Dic22#9914yescomplemented
209C11⋊C8—42no—
210C11⋊C8—81no—
211C23×Q8—111no—
212C22×SD16—112no—
213C2×#121C2×D1111yescharacteristic
214C2×C4×Q8—221no—
215#448—221no—
216#448—222no—
217#448—221no—
218C2×#103—112no—
219C2×#103—222no—
220C2×#99—21no—
221C2×#99—21no—
222C2×C22⋊C8—111no—
223C2×C22⋊C8—111no—
224#391—222no—
225#391—221no—
226#380—111no—
227#380—221no—
228#380C2×D1111yescharacteristic
229C4×C22⋊C4—221no—
230C4×C22⋊C4C2×D1111yescharacteristic
231#327—222no—
232C22×C11—21no—
233C22×C11—21no—
234C22×C11—21no—
235C22×C11—21no—
236C22×C11—21no—
237C22×C11—21no—
238C22×C11—41no—
239C22×C11—41no—
240C22×C11—41no—
241C22×C11—41no—
242C22×C11—81no—
243C22×C11—81no—
244C22×C11—81no—
245C22×C11—161no—
246C22×C11—161no—
247C22×C11#38611yescharacteristic
248C22×C11C4×SD1611yescharacteristic
249C22×C11#44011yescharacteristic
250C22×C11#44811yescharacteristic
251C22×C11#44911yescharacteristic
252C22×C11#46011yescharacteristic
253C22×C11#46411yescharacteristic
254C4×C11—21no—
255C4×C11—21no—
256C4×C11—21no—
257C4×C11—42no—
258C4×C11—81no—
259C4×C11—81no—
260C4×C11—161no—
261C4×C11C2×#9912yes—
262Dic11—24no—
263Dic11—42no—
264Dic11—82no—
265C22×Q8—112no—
266C22×Q8—111no—
267C22×Q8—112no—
268C22×Q8—111no—
269C22×Q8—221no—
270C22×Q8—221no—
271C22×Q8—221no—
272C22×Q8—444no—
273C22×D4—21no—
274C22×D4C4×D1111yescharacteristic
275C23×C4—221no—
276C23×C4C22×D1111yescharacteristic
277C2×SD16—222no—
278C2×SD16—222no—
279C2×SD16—444no—
280C22×C8—112no—
281C22×C8—221no—
282#121—21no—
283#121—21no—
284#121—21no—
285#121—21no—
286C4×Q8—444no—
287C2×C4⋊C4—21no—
288C2×C4⋊C4—222no—
289C2×C4⋊C4—221no—
290C2×C4⋊C4C4×D1111yescharacteristic
291C2×C22⋊C4—21no—
292C2×C22⋊C4—21no—
293C2×C22⋊C4—221no—
294C2×C22⋊C4C22⋊D1111yescharacteristic
295C2×C22⋊C4C22⋊D1111yescharacteristic
296C2×C42—21no—
297C2×C42—222no—
298#103—222no—
299#103—222no—
300#103—444no—
301#99—42no—
302#99—42no—
303C22⋊C8—221no—
304C22⋊C8—221no—
305C22⋊C8—221no—
306C22⋊C8—221no—
307#95—21no—
308#95—21no—
309#95—112no—
310#95—222no—
311#95—222no—
312C2×C11—21no—
313C2×C11—21no—
314C2×C11—21no—
315C2×C11—21no—
316C2×C11—21no—
317C2×C11—21no—
318C2×C11—161no—
319C2×C11#188011yescharacteristic
320C2×C11#189811yescharacteristic
321C2×C11#190511yescharacteristic
322C24—21no—
323C24C2×C22⋊D1111yescharacteristic
324C2×Q8—112no—
325C2×Q8—112no—
326C2×Q8—224no—
327C2×Q8—224no—
328C2×Q8—224no—
329C2×Q8—222no—
330C2×Q8—221no—
331C2×Q8—221no—
332C2×Q8—222no—
333C2×Q8—442no—
334C2×Q8—442no—
335C2×Q8—442no—
336C2×Q8—444no—
337C2×Q8—444no—
338C2×Q8—444no—
339C2×D4—21no—
340C2×D4—21no—
341C2×D4—42no—
342C2×D4—41no—
343C2×D4—41no—
344C2×D4—41no—
345C2×D4—41no—
346C2×D4—41no—
347C2×D4—41no—
348C22×C4—21no—
349C22×C4—21no—
350C22×C4—21no—
351C22×C4—42no—
352C22×C4—41no—
353C22×C4—221no—
354C22×C4—222no—
355C22×C4—221no—
356C22×C4—222no—
357C22×C4—222no—
358C22×C4—444no—
359C22×C4C2×C4×D1111yescharacteristic
360C22×C4#433911yescharacteristic
361C22×C4D4×D1111yescharacteristic
362C22×C4D4×D1111yescharacteristic
363C22×C4D4×D1111yescharacteristic
364C22×C4#434111yescharacteristic
365SD16—444no—
366SD16—444no—
367C2×C8—222no—
368C2×C8—442no—
369C2×C8—442no—
370C2×C8—441no—
371C4⋊C4—21no—
372C4⋊C4—21no—
373C4⋊C4—42no—
374C4⋊C4—442no—
375C4⋊C4—444no—
376C22⋊C4—21no—
377C22⋊C4—21no—
378C22⋊C4—21no—
379C22⋊C4—41no—
380C22⋊C4—41no—
381C22⋊C4—41no—
382C22⋊C4—41no—
383C22⋊C4—441no—
384C22⋊C4—441no—
385C22⋊C4#432412yescomplemented
386C42—42no—
387C42—444no—
388C11#926211yescharacteristic, complemented, Sylow
389C23—41no—
390C23—41no—
391C23—41no—
392C23—41no—
393C23—41no—
394C23—81no—
395C23—81no—
396C23C4×C22⋊D1111yescharacteristic
397C23#6698511yescharacteristic
398C23C2×#432411yescharacteristic
399C23#6699011yescharacteristic
400C23#6699111yescharacteristic
401C23#6700311yescharacteristic
402C23#6700411yescharacteristic
403Q8—114no—
404Q8—224no—
405Q8—222no—
406Q8—222no—
407Q8—222no—
408Q8—444no—
409Q8—444no—
410Q8—442no—
411D4—42no—
412D4—81no—
413D4—81no—
414D4—81no—
415D4—81no—
416D4—81no—
417C2×C4—22no—
418C2×C4—22no—
419C2×C4—22no—
420C2×C4—22no—
421C2×C4—41no—
422C2×C4—41no—
423C2×C4—41no—
424C2×C4—41no—
425C2×C4—41no—
426C2×C4—41no—
427C2×C4—41no—
428C2×C4—41no—
429C2×C4—41no—
430C2×C4—41no—
431C2×C4—41no—
432C2×C4—81no—
433C2×C4—81no—
434C2×C4—81no—
435C2×C4—224no—
436C2×C4—222no—
437C2×C4—222no—
438C2×C4—444no—
439C2×C4—444no—
440C2×C4—442no—
441C2×C4—442no—
442C2×C4—442no—
443C2×C4—442no—
444C2×C4C22⋊C4×D1111yescharacteristic
445C2×C4(C22⋊D11)⋊C411yescharacteristic
446C2×C4#6693611yescharacteristic
447C2×C4#6693711yescharacteristic
448C8—442no—
449C8—881no—
450C22—21no—
451C22—21no—
452C22—21no—
453C22—21no—
454C22—21no—
455C22—21no—
456C22—41no—
457C22—41no—
458C22—41no—
459C22—41no—
460C22—81no—
461C22—81no—
462C22—81no—
463C22—161no—
464C22—161no—
465C22#1062256911yescharacteristic
466C22C4×#432411yescharacteristic
467C22#1062263111yescharacteristic
468C22#1062265011yescharacteristic
469C22#1062265311yescharacteristic
470C22#1062266711yescharacteristic
471C22#1062268811yescharacteristic
472C4—21no—
473C4—21no—
474C4—21no—
475C4—42no—
476C4—81no—
477C4—81no—
478C4—161no—
479C4—224no—
480C4—442no—
481C4—882no—
482C4D11×#9912yes—
483C2—21no—
484C2—21no—
485C2—21no—
486C2—21no—
487C2—21no—
488C2—21no—
489C2—161no—
490C2#1306897411yescharacteristic
491C2#1306906611yescharacteristic
492C2#1306911311yescharacteristic
subgroupG/H
centerC22#10622569
commutatorC22×C4×C11C22×C4
FrattiniC23×C4C22×D11
FittingC11×#1964C2
socleC22×C11#386
prime radicalC2×C11×#121C22
cosocleC23×C4×C11C23
hypercenter#1964D11
hypocenterC11#9262
LCSG ▷ C22×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C23×C4 ◁ #1964

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
2. C22⋊C4×Dic22C2semidirect
3. #13068550C2semidirect
5. #13066483C2semidirect
6. #13066464C2semidirect
10. C22×#4324C4semidirect
23. C2×#66874C4semidirect
130. C11×C22⋊C4SD16semidirect
208. Dic22#99semidirect
385. C22⋊C4#4324semidirect
388. C11#9262semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
C2×#106226532
C22⋊C4×Dic222
#130685502
#130671842
#130664832
#130664642
C11×#19642
#926211